Work

Sup-slopes and sub-solutions for fully nonlinear elliptic equations

Year: 2024

Type: preprint

Abstract: We establish a necessary and sufficient condition for solving a general class of fully nonlinear elliptic equations on closed Riemannian or hermitian manifolds, including both hessian and hessian quotient equations. It settles an open problem of Li and Urbas. Such a condition is based on an analytic slope invariant analogous to the slope stability and the Nakai-Moishezon criterion in complex geometry. As an application, we solve the non-constant $J$-equation on both hermitian manifolds and singular Kähler spaces.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2405.03074

Authors: Guo, Bin, Song, Jian

Institution: Rutgers, The State University of New Jersey

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Differential Equations in Complex Riemannian Geometry, Canonical Kahler metrics and complex Monge-Ampere equations

OpenAlex ID: W4396743247

Cites:

Cited by:

Related to: 10